Suppose an electric utility is considering whether to install a wind farm with 20 megawatts (Mw) of capacity instead of a natural gas plant that would generate the same amount of annual electricity. An engineering study showed that the site for the wind farm would produce a load factor of 25 percent. (Actual generation would be 25 percent of capacity on average over the course of a year.) The natural gas plant could be operated with a load factor of 50 percent. Capital costs for the wind farm would $1.5 million per megawatt, compared to $1.0 million per megawatt for the natural gas plant. Operating costs for both plants would be $2 million per year excluding fuel costs.
a. If the gas plant has a thermal efficiency of 0.4 (that is, 40 percent of the energy in the fuel gets converted to electric energy), and the cost of natural gas is $4 per million Btu, how much natural gas would be needed, and what would be the annual fuel cost for the gas plant? Show your calculations, including the assumptions you make about converting Btus to Mwh.